Pyrotron thermonuclear reactor and process



Feb. 23, 1965 R. F. POST PYROTRON THERMONUCLEAR REACTOR AND PROCESS Filed July 14, 1954 9 Sheets-Sheet 2 IN V EN TOR.

RICHARD F POST BY ATTORNEY.

Fab.v 23, 1 965 R. F. PCST PYROTRDNi THERMO'NUCLZEAR REACTOR AND PROCESS Filed". July. 14, 1954-.

9 Sheets-Sheet 3' Negatively Charged (Electrons) Positively Charged (Ions) 9 R0 WP F D N.R

A H w R ATTORNEY.

Feb. 23, 1965 R. F. POST 3,170,841

PYROTRON THERMONUCLEAR REACTOR AND PROCESS Filed July 14, 1954 9 Sheets-Sheet s I 3 5 6 7 8 9 IO Magnetic field sfrength, H. units of IO" guuss H (units of IO gauss) IOOO RICHARD F. POST BY ATTORNEY Feb. 23, 1965 R. F. POST 7 PYROTRON THERMONUCLEAR REACTOR AND PROCESS Filed July 14, 1954 9 Sheets-Sheet 7 ATTORNEY.

1965 R. F. POST 3,170,841

PYROTRON THERMONUCLEAR REACTOR AND PROCESS Filed July 14, 1954 9 Sheets-Sheet 8 ENERGIZING CURRENT SUPPLY TRIGGERED PULSE 3 GENERATOR INVENTOR.

RICHARD Posr BY ATTORNEY.

Feb. 23, 1965 R. F. POST PYROTRON THERMONUCLEAR REACTOR AND PROCESS Filed July 14, 1954 9 Sheets-Sheet 9 E 25 22L 2 332 322mm Accumulator Zone Reaction Zone l Q R E W O P DELAY SOURCE INVENTOR.

RICHARD F. POST flaw/ M ATTORNEY United States Patent v 3,170,s4t PYROTRON THERMONUCLEAR REACTOR AND PROCESS Richard F. Post, Walnut Creek, Califl, assignor to the United States of America as represented by the United States Atomic Energy Commission Filed July 14, 1954, Ser. No. 443,447 30 Claims. (Cl. 176--5) The present invention relates generally to the thermonuclear field, i.e., to that class of nuclear reactions which occur at very highly elevated temperatures and with corresponding confinement pressures. More particularly, the invention relates to methods and apparatus for conducting controlled thermonuclear reactions, whereby manifold utilitarian purposes may be served.

Speculation as to the possibility of conducting terrestial thermonuclear reactions had its beginning with the original proposal of Atkinson and Houtermans (Zeit. f. Phys. 54, 656 (1928)) that the source of stellar energy was thermonuclear. A few early suggestions considered the use of high-energy discharge methods or some modification thereof. However, no proposal of demonstrable feasibility appears in the literature.

With reference to nuclear reactions, generally, it may be noted that nuclear chain fission reactions of certain heavy isotopes, wherein neutrons are the fission-inducing agents which neutrons are reproduced in excess of those initiating the reaction, are more or less self-propagating when merely a proper geometrical critical mass arrangement of components is provided. Thermonuclear reactions on the other hand are more nearly like temperatureinduced chemical reactions than are the nuclear chain reactions, in that a volume element of reactant material must be heated to a high temperature and, in order that the reaction be sustained or be propagated, the reaction ratein this volume must be sufficient to balance the energy loss or be sufficient to heat neighboring volume elements, respectively. Otherwise, the reaction is quenched, i.e., the rate diminishes to zero.

Some analogies exist between the thermodynamics of chemical reactions and the thermodynamics of thermonuclear reactions. In chemical chain reactions, e.g., the ordinary reactions of chemistry, the activation energy is of the order of one volt which means that these reactions will proceed with great rapidity if the system is preheated to a few thousand degrees and in favorable circumstances, e.g., with appropriate catalysis, with much lower temperatures. Moreover, a considerable reaction rate which'obeys certain statistical laws is permitted by the phenomena of penetration of the activation energy barrier, a phenomena which is very sensitive to temperature changes. As a consequence, many inorganic and a few organic chemical reactions proceed at such a rate, that, in ordinary reactions, the rate seems almost instantaneous, i.e., due to high reactant densities. -With organic chemical reactions, generally, the rate is slow or almost non-existent, at room: temperatures and increases markedly with increase in temperature. Chemical reactions involve only the outermost valence electrons of the reacting atoms which electrons are available with little difiiculty and with relatively little repulsion permitting approach of reacting atoms at relatively low velocities.

On the other hand, the energy (related to the approach velocity) necessary to cause two nuclei to approach sutliciently close for thermonuclear fusion of the nuclei to occur is of the order of one Mev. (million electron volts). It is therefore extremely unlikely that such a reaction can be initiated by chemical energy means alone. The potential or coulomb barrier between nuclei which is due to the mutually repulsive positive charge residing thereon requires a great deal of energy to overcome and,

moreover, the potential barrier between heavy nuclei is proportionally much greater than between light nuclei, i.e., those with fewer nuclear protons. However, quantum mechanical leakage, i.e., penetration, of these barriers may proceed to an appreciable degree at somewhat lower temperatures. Furthermore, studies, e.'g., of thermonuclear fusion reactions in'the stars, have shown that quantum mechanical barrier porosities effectively reduce the activation energy'belo'w the coulomb barrier energy. Therefore, kinetic temperatures (of'the order of about 10 to 10 degrees Kelvin) equivalent to a few of tens of kilo-electron-volts (kev.) should, under appropriate circumstances and especially with certain light elements, be sufiicient to initiate a thermonuclear reaction.

Under normal circumstances in a population of energetic particles at ordinary material densities the energies of the individual particle, i.e., the temperatures thereof, are represented by a ther'malized or Maxwellian equilibrium distribution and the system is in radiation equilibrium. With such a system it is difficult to increase the temperature to the required degree since all of the particles present, e.g., neutral atoms, ions, electrons and photons must all be heated to a very high average temperature and in the face of all the loss processes to provide a sufiicient number of particles with the energy necessary to initiate the reaction. The reaction system at the tem peratures contemplated herein will comprise a tenuous system of highly ionized atoms and about an equivalent number, chargewise, of electrons, since all matter at these kinetic temperatures is essentially completely ionized. The system will not be in radiation equilibrium because of the tenui-ty thereof; therefore, heating of the plasma is more simple and the reaction more easily sustained. Throughout the description of the invention, the term plasma will be employed to designate such a tenuous system of highly-ionized atomic nuclei and the associated electrons, generically, with context relied upon to convey more specific meaning.

The controlled thermonuclear process of my invention basically contemplates the establishment of a plasma comprising appropriate thermonuclear reactants wherein the fuel ions have a high kinetic energy, the containment of such plasma by magnetic field means, introduction (injection( trappings an accumulation of energetic thermonuclear reactant particles (fuel ions) within the reaction zone, and heating, i.e., increasing the kinetic energy of the contained reactants, so as to promote, establish and/or maintain a thermonuclear reaction. It is further contemplated that such reaction will be employed to accomplish manifold purposes including the production of heat, power, energetic nuclear particles and the use of such particles for promoting nuclear reactions, with or without attendant production of heat and power, the direct conversion of the energy derived from the thermonuclear reaction into electrical energy, synthesis of isotopic species and others which will be apparent from the following description.

More particularly, in the process of my invention the thermonuclear reaction is conducted in a vacuum, i.e., a region from which extraneous neutral gaseous materials are evacuated to a sutlicient degree to prevent interference with the progress of the reaction. Firstly, provision is made for the containment of the reaction plasma within such evacuated region by establishing therein a manipulated magnetic field, preferably, a magnetic field which is axially symmetric, i.e., one which is radially symmetric about an axis which is conveniently considered a longitudinal axis. Of prime importance for accomplishing the purposes of the invention, such-magnetic field is provided in such a manner that the intensity of the magnetic field in longitudinally spaced regions or nodal regions is gradientially increased, while in the intervening space between these regions of increased magnetic intensity the field is of relatively lower intensity. A magnetic field, so provided, may be considered to establish a containment zone in which an energetic charged particle will be effectively retained for considerable periods. Such reaction zone being situated within the intervening space between the gradientially increased regions, whereby the contained particles describe helical paths more or less coaxially oriented or parallel with the longitudinal axis of the said magnetic field and are alternately reflected by the gradientially increased magnetic field regions. Such gradientially increased magnetic fields may, therefore, be considered to be terminal reflectors or closures of the containment zone while the central portions of the magnetic field provide radial closure. It will be understood that, in this region, charged particles of whatever origin or method of introduction and with energies within the capabilities of the magnetic containment means would be contained therein. Depending on the function being served such containment zone may be designated in the specification by other terms, the meaning of which will be apparent from context and such zones may be employed singly or in plurality as required for hereinafter disclosed methods of operation.

Secondly, provision is made for the introduction of thermonuclear fuel ions into the containment zone. Ions may be formed in situ therein or may be introduced and accumulated or collected within the containment zone from external sources by certain methods, the necessary features of which will be more fully described hereinafter. However, preferred methods of injection may be accomplished by utilizing external ion source means providing an accelerated space-charge neutralized beam of the fuel ions directed into appropriately determined locations of the magnetic field correlatively with hereinafter described manipulation of the positions and intensities of the aforesaid reflector regions. By virtue of these manipulative operations a plasma charge of the ionic fuel, preferably having an energy distribution skewed in favor of a high proportion of the more energetic components, is trapped and accumulated in the aforesaid reaction zone, whereby, as the density increases above a minimum value, thermonuclear fusion reactions may begin and proceed at an appreciable rate.

In this connection it may be noted that considerable energy can be imparted to the introduced fuel ions. While it is practicable to inject such particles with suflicient energy to immediately initiate the thermonuclear reaction (when adequate densification is achieved by injection), it is often preferred, at least initially, to inject the particles, as allowed by features of the present invention, at a lower temperature to be trapped and accumulated under conditions wherein losses and thermalization occur at materially reduced rates. Additional energy is later applied to elevate the temperature of these preheated particles to the reaction temperature and/or the plasma is densified, e.g., as by compression, to initiate, establish and/or promote the reaction. A very important consideration in selecting the ion source means employed in injecting the ionic fuel is that little extraneous gaseous material be simultaneously injected since these materials tend to unduly increase energy loss by thermalizing and radiative processes. Furthermore, it is desirable that the energy distribution of the particles contain few low energy (low temperature) groups, particularly groups which are considerably below preheat temperature, since the present method preserves, for a very appreciable time, these non- Maxwellian ionic temperature distributions, whereby the initiation and sustenance of the thermonuclear reaction is greatly facilitated.

Thirdly, provision is made for heating of the accumulated preheated charge by adiabatic compression obtained by increasing the intensity of the overall magnetic field favoring a sharper increase in the reflector regions and by causing such reflector field regions to move proximally along the longitudinal axis. The inward movement of the reflector regions and overall increase of magnetic field intensity of the containment zone produce both radial and axial compression of the plasma reactant charge. The attendant adiabatic heating of the preheated particles and the forcing of the reactant ions into a severely limited region establish the conditions requisite to the initiation and/ or promotion of the thermonuclear reaction with such reaction then continuing with a tremendous exothermic release of energy and production of nuclear particles, utilizable as set forth hereinafter. Auxiliary heating methods may be employed therewith, e.g., radiofrequency electromagnetic radiation and especially microwaves may be applied at certain stages of the operation.

Appropriately, a fourth operation, i.e., decompression, is provided by manipulation of the magnetic field, whereby the plasma is allowed to expand after initiation, during and/or on completion of the reaction to obtain various beneficial effects. Such expansion may be employed to reduce and, therefore, regulate the rate of the reaction while in progress. As a prime feature, however, the decompression may be employed to convert the charged particle energy produced by the reaction and recover energy supplied to the magnetic field and particles on injection and compression, as will be described more fully hereinafter.

The invention also provides apparatus in which the processes of the invention may be conducted, such apparatus comprising, in general, means for establishing an evacuated spacial region, means for establishing the indicated magnetic fields within the evacuated region, means for supplying the electrical energizing currents for the said magnetizing means, said magnetizing means and/ or electrical energization means comprehending further means for causing correlated movement of the reflector field regions and for correlating magnetic field intensities as required by hereinafter disclosed operational schemes, and thermonuclear fuel injection means. Accessory apparatus for utilizing the nuclear particles, heat, kinetic energy of the combustion products, other products and/ or effects of the reaction are also provided. Continuous, pulsed, single phase, multiphase and cyclic modes of operation for accomplishing the foregoing are contemplated. Apparatus of the character disclosed herein is now identified by the generic term Pyrotron.

Accordingly, it is an object to provide methods and :tpparatus for conducting controlled thermonuclear reacions.

Another object of the invention is to provide a process for conducting a thermonuclear reaction wherein the reaction zone is confined within a magnetic field which is characterized by displaying symmetry about an axis.

A further object of the invention is to provide methods and apparatus for conducting thermonuclear reactions wherein a magnetic field having general symmetry about a longitudinal axis is employed for radial confinement and longitudinally-spaced, gradientially-increased magnetic field regions thereof provide axial confinement of thermonuclear reactants the combination of said magnetic fields defining a thermonuclear containment zone centrally disposed about the axis thereof.

Still another object of the invention is to provide methods whereby ions with a high kinetic energy may be in jected and trapped in a containment zone provided in an axially symmetric magnetic field having spaced gradientially intensified reflector field regions.

Another object of the invention contemplates the initiatlon and/or promotion of a thermonuclear reaction by providing densification and heating of a tenuous fuel plasma charge.

A very important object of the invention is to providemethocls and apparatus for conducting a thermonuclear reaction wherein the field intensities of radial confining and gradientially increased magnetic reflector field regions are increased to produce compression of a thermonuclear fuel plasma contained therein.

A further object of prime importance is to provide methods and apparatus for conducting a thermonuclear reaction wherein longitudinally-spaced, gradientially-increased magnetic reflector field regions are caused to move proximally and/ or together with magnetic field intensification to effect accumulation and compression of a contained plasma fuel charge.

Another important object of the invention is to provide methods and apparatus for introducing a thermonuclear fuel in a preheated ionic form in order to minimize certain difficulties of non-preheated fuel charges and in order to increase the effectiveness of subsequent heating to thermonuclear reaction temperatures.

Still another object of the invention is to provide operational schemes wherein the injection of thermonuclear fuel ions is correlated with predetermined variations of the magnetic fields so as to cause the introduced fuel to be trapped in a magnetically defined containment zone.

An extremely important object of the invention is to convert energy produced in the reaction and residing in energetic charged particles into electrical energy for use in an external electrical circuit.

Other objects of the invention relate to the production of heat, nuclear and other elemental particles, synthesis of elemental materials, and utilization of energetic neutrons and other utilitarian products of a thermonuclear reactor.

Still further objects of the invention relate to the use of a plurality of containment and/or reaction zones in mutually phased and correlated fashion to provide sustained operating characteristics and other advantageous features.

Still other objects of the invention relates to the provision of accessory equipment and methods of utilizing the various products and effects produced in controlled thermonuclear reactions.

Other objects and advantages of the invention will become apparent by consideration of the following description taken in conjunction with the accompanying drawings, of which:

FIGURE 1, portion (a), is an illustration of a particle .path in a magnetic field containment-zone provided in accordance with the invention and portion (b) is a graphical illustration of typical magnetic field intensity profile along the axis of said zone with portion (b) disposed in corresponding position beneath portion (a);

FIGURE 2 is a vectorial diagram indicating various relationships of particle velocities and magnetic field inten sities employed in determining the angle of exclusion of particles from a reflector field;

FIGURE 3 is a diagram illustrating relationships employed in calculating the solid angle of particle loss through a reflector field;

FIGURE 4-, portion (a), schematically represents a containment zone and portion (b) is a graphical representation of a corresponding magnetic field intensity profile along the axis therein which profile is of importance in a preferred method of injecting and trapping an ionic fuel charge in the containment zone;

FIGURE 5 is a vectorial diagram of certain particle velocity relationships of importance in accomplishing injection, trapping and accumulation of an ionic fuel charge in the containment zone;

FIGURE 6 is a graphical illustration of the variation of magnetic reflector field intensity profiles as employed in a second preferred method for injecting an ionic fuel into the containment zone;

FIGURE 7 is an illustration of the relative motions of negatively and positively charged particles in crossed magnetic and electrostatic fields;

FIGURE 8 is an illustration of a radial cross section of the electrostatic field generated in an axially symmetric magnetic field which is varying in intensity as a function of time;

FIGURE 9 is a graphical representation of the variation in thermonuclear reaction cross section for certain hydrogen isotopes;

FIGURE 10A illustrates a typical particle orbit early in compression and FIGURE 10B illustrates a typical particle orbit later in compression, relevant to the compressive adiabatic heating process of the invention;

FIGURE 11 is a vectorial diagram of particle path relationships in a magnetic field;

FIGURE 12, portion (a), indicates relationships of a particle before reflection and portion (b) indicates the relationships of a particle after reflection by a magnetic reflector field, as utilized in a theoretical explanation of the reflection phenomena;

FIGURE 13 is an illustration of relationships employed in determining the collision times of particles in the containment zone;

FIGURE 14, portion (a), illustrates particle angular distributions immediately following a rapid compression cycle; portion ([2) the distribution a short time later; portion (c) the distribution which would be obtained with no losses at the reflector fields; and portion (d) a comparison of early and late distributions, the latter being indicative of relative distributions when loss begins to increase seriously;

FIGURE 15 is a graphical illustration of a typical equilibrium density distribution of plasma particles across a diameter of the containment zone;

FIGURE 16 is a graphical illustration of possible magnetic field densities as distributed across a diameter of the containment zone;

FIGURE 17 illustrates dimensional relationships of a solenoidal coil structure relevant to calculation of losses therein;

FIGURE 18 graphically illustrates the electrical power per unit length required to energize a solenoid as a func tion of magnetic field intensity;

FIGURE 19 graphically illustrates typical values for thermonuclear power, P,,, bremsstrahlung loss, P and magnet power, P (at limiting densities), as a function of the centrally applied magnetic field in a thermonuclear reactor;

FIGURE 20 illustrates dimensional relationships of a solenoid which are employed in calculating the unperturbed energy storage of solenoids employed to establish the containment fields;

FIGURE 21 is a semi-diagrammatic illustration of basic components of a single-zone thermonuclear reactor suitable for conducting a thermonuclear reaction in accordance with the invention;

FIGURE 22, portion (a),is a semi-diagrammatic illustration of basic components of a multiple zone thermonuclear reactor, and portion (12) a graphical representation of the axial magnetic field intensity profile employed therein at a particular period in the cyclic operation;

FIGURE 23A is a semi-diagrammatic illustration of a reactor embodiment in which the final reaction zone is contained by fields produced by solenoids of a diameter small as compared to those employed in the accumulator zone and FIGURE 23B is a graphical illustration of the axial magnetic field intensity profile employed therein as during injection.

FIGURE 24A indicates the reactor of FIGURE 23, after compression, and FIGURE 24B is a graphical representation of the axial magnet field intensity profile as employed therein;

FIGURE 25 is a diagrammatic illustration of a multiple zone continuous closed loop thermonuclear reactor system;

FIGURE 26 is a side elevation of a single zone thermonuclear reactor in accordance with the invention;

FIGURE 27 is a vertical cross sectional view of the reactor of FIGURE 26; and

FIGURE 28 is a circuit wiring diagram employed with the reactor of FIGURE 26.

It will be of assistance to, at the outset, consider thermonuclear reaction and the nuclear processes which occur in such reactions. For a variety of practical and theoretical reasons it is considered that isotopes of hydrogen, especially deuterium, D, and tritium, T, are preferred fuels while other light elements and isotopes, e.g., He Li, Be and others selected from the light nuclide portion of the mass defect curve, may also be employed either singly or in admixture. Moreover, a variety of such light elements as Well as heavy elements, particularly fissionable materials including slow and fast neutron fissionable materials, may be employed in accessory or subsidiary manners to utilize products derived of the controlled thermonuclear reaction, e.g., as in fission, transmutation, fuel regeneration, and other nuclear processes. For the sake of brevity, illustrative reference will be made to reactions which occur with hydrogen isotopes and certain products which are derived therefrom; however, it will be understood that the teachings of the invention will apply equivalently to the other materials noted above.

The availability of deuterium in nature is sufficient to support a tremendous power output. While deuterium comprises only about 1 part in 5000 of terrestial hydrogen, the energy derivable from this amount of deuterium causes each gallon of water to be equivalent, energy-wise, to about 300 gallons of gasoline. Since there is about 10 gallons of water on earth, this is equivalent to about 3 10 gallons of gasoline.

Estimates have established the total electrical power output from all world sources at about 10 megawatts. If this rate were increased by a factor of (possible in a century) irreplaceable sources, such as the known fossil energy sources, would be exhausted in the relatively short time yet the deuterium supply would last indefinitely as shown by the following ideal efficiency estimative calculation:

l0 megawatts: 10 joules/ second and the deuterium supply, used at this rate, would last 4.0Xl0 4=.0 10 10 v 4.0 l0 (sec.)1.3 10 years gQ VHE -ln 3.25 Mev',

2, 13+- +4..o ne

D spi s n6 +p +1803 new.

Whenever a D-D reaction occurs which produces a triton, T, the triton will almost hnmediately react with another deuteron. Also at the high He energies which result from the reaction, the value of 0', the reaction crosssection, of the D-H reaction becomes considerably larger than that of D-D and so that most of the He will also burn promptly. it will be apparent therefrom that He and T, either alone or in admixture with D, would be valuable fuels if available from exterior sources or produced regeneratively within the reactor.

Totaling up the yields, which are obtained in a D-D, thermonuclear reaction, there is obtained:

For comparison, note that if the TD reaction alone is used, the yield for each triton or deuteron burned is The division of kinetic energy between the products of the reactions is also of importance. Of this energy nearly all of that residing in the kinetic energy of the charged particles will remain in the containment zone while the energetic neutrons will, of course, depart from the system and, therefore, may be utilized externally of the containment zone to produce nuclear reactions as described hereinafter. For example, per deuteron reacting one obtains kinetic energies for charged (W and neutral (W particles;

Thus it is seen that, in general, more energy will appear in the form of kinetic energy of the charged particles than in the form of kinetic energy of the neutrons. It is therefore apparent that methods of eiliciently recovering the charged particle energy would provide a major source of power. It is instructive to note that the calculated energy yield per gram of deuterium amounts to about 3.4 10 joules or about 3.5 times as much energy per unit weight as may be obtained from fissionable materials and without the production of large amounts of troublesome fission products.

The various operational steps of the process of the invention, viz., containment, injection, compression and decompression, described briefly above, will now be discussed, in detail, hereinafter.

CONTAINMENT As disclosed above, the fuel comprising the thermonuclear reactant fuel charge is in the form of a plasma, i.e., atomic species in a highly ionized gaseous state. Solid containment walls would either disintegrate or unduly cool the reactants; therefore in operating the process of the invention, magnetic fields are employed to contain the reactant charge. However, at an appropriate position exteriorly of the containment zone, solid material surfaces and structures may be employed to provide an evacuated spacial region in which is disposed such thermonuclear containment zone; likewise solid secondary reactants, heat transfer surfaces and the like may be disposed in close proximity about the magnetic containment zone to serve various purposes. For example, radiatron-absorptive, heat transfer surfaces, thermonuclear fuel regeneration substances, target materials for nuclear transmutation, fissionable materials, subcritical neutron reactor assemblies, and the like, may be so disposed. While such magnetic fields may be manipulated to accomplish various purposes and are dynamically influenced by the course of the reaction, it will be convenient to describe various operations including containment by reference to instantaneous and, therefore, essentially momentarily static magnetic field conditions which are easily portrayed graphically and are easily generalized.

A magnetically contained thermonuclear reaction zone may be provided, in accordance with the invention, as illustrated in FIG. la, of the accompanying drawing. Only a generally cylindrical elongated central region of the entire magnetic field, e.g., the portion enclosed by the solenoid producing the field, is considered, since it is only these portions which were primarily concerned in defining the containment zone. More particularly, the magnetic field which defines the containment zone is preferably provided by any suitable means in such a manner that the field intensity patterns in radial planes about an 'axisare generally symmetrical, i.e., in such a manner that the field intensities are substantially axially symmetric. Moreover, such fields are provided with a relatively elongated central region along which the magnetic field intensity, H is approximately uniform as indicated in corresponding portions of the magnetic field intensity profile of FIG. 1b, and which merge smoothly with gradientiallyincreased terminal magnetic intensity, reflector field regions, H and H A charged energetic particle, i.e., one which has a finite velocity with radial and axial'components and other distinctive class properties and which is produced in situ or introduced into such a field, in accordance with hereinafter described methods, will be contained in such field. Such particle will describe the typical helical path illus trated in FIG. la, having an axis of rotation generally parallel with the longitudinal axis of the said field, i.e., parallel to the magnetic lines of force. It will be appreciated that the actionof a particle in the presence of a dense plasma will differ markedly from the simplification noted above; nevertheless, on a statistical average,

the bulk of a plasma is effectively contained. The zone of containment may be visualized as being generally cylindrical, as being coaxially disposed within the central portions of the magnetic field and with the terminal regions of the zone being constricted, i.e., closed in the regions of the reflector fields H and H Such a field may be provided by various equivalent means, 'e.g., by means of an electrically-energized, elongated solenoid, axially aligned solenoid segments, toroidal solenoidal windings (in curved reactor sections), etc., whereby, the magnetic field regions and especially the containment zone, of FIG. 1a, would be concentrically enclosed therein. The approximately uniform field portion,

H may be obtained merely by disposing the solenoidal windings so as to uniformly distribute the ampere turns effective in this region while the gradientially-intensified reflector field regions may be provided merely by increasing the ampere turns of the solenoid effective in these regions as by overlapping layers of conductor, using overlapping solenoids segments and/ or increasing the electrical current in the solenoid portions efiective in these regions. Other means may be employed as auxiliary aids, at least, in shaping the fields.

CONTAINMENT Theory .Containment, which has been demonstrated in practical operation, is explainable on theoretical bases as follows: First, consider a perturbation treatment of the motion of a particle in a magnetic field, H, wherein it is assumed:

where r=radius of gyration and T=cyclotron period.

The above assumes that the change of H in time and space is small during transit of one revolution of the helical path; a condition which is more nearly approached in large containmentlsystems. The second condition will be very well satisfied for all cases of interest in the present disclosure; however, qualitatively, the approximations do not materially afiect the results. With the above conditions satisfied the paths of the individual particles in the field will be helices in which the center of rotation is along the magnetic lines of force. We may then consider the total kinetic energy of the particle, W, as divided into two vectorial partsa rotational energy, W,, from motion perpendicular to the magnetic field and a translational 10 energy, W from motion parallel to the field, so that at all times:

W=W,+W

m'=mass of particle r=radius of rotation H :magnetic field intensity ezcharge c=velocity of light This can be rewritten as n where a is the angular momentum of the particle in its helical orbit. Now in the perturbation limit, it is apparent that the angular momentum about the center of rotation of the particle is constant since the magnetic forces are all exerted perpendicular to the circular motion of the particle. Thus it may be seen that wherein a=magnet1e moment; of the particle The conditions for reflection of a particle at the terminal magnetic field regions, i.e., axial containment, can now be deduced by simply considering the conservation of energy and the effect of over the region between the planes x=0 and H(x) where H(0)=field intensity at x=0 in the central region and H(x)=field intensity in the reflector field region (Bi as indicated in FIG. 1a.

As a consequence of the fact that constant constant with a contained particle moving into a region of intensified magnetization, W, must increase at the expense of W since the total kinetic energy, W=W |W,, must be conserved on the average. Thus the axial motion of the particle in the original direction is diminished to the vanishing point and the particle reverses the axial direction of travel with a simultaneous transferal of kinetic energy, i.e., W, to W This is a general consideration satisfied whenever a moving charged particle is encountering an intensified field of sufiicient magnitude.

We have thus:

It will be noted that this equation indicates that as a particle moves into a region of intensified magnetization the axial component of energy is continually diminished until, if H(x) is of suflicient magnitude, such axial component finally vanishes, at which time the particle is stopped and the direction of travel along the axis of the containment field is reversed, whereby the particle is alternately reflected between the magnetic reflector field regions H and H and is, therefore, eflectively contained. This behavior is also apparent from the viewpoint that a rotating charged particle has a magnetic moment such that it is always repelled from a region having an intensifled magnetic field. Also, the cause of the reflection be comes apparent if one notes the direction of the lines of force in traversing a zone of increasing magnetic intensity.

The condition governing reflection may be derived merely by equating the expression (II), to zero, i.e., representing the time at which the particle comes to rest and spirals back out of the region of intensified magnetization H(x) as shown in FIG. 1a and in accordance with the following considerations:

and II(x) is the field strength at the point of reflection, x. The value R will be known hereinafter as the reflector ratio, i.e., ratio of reflector field intensity to central axial field intensity in the magnetic containment zone. It will be apparent that the points, x, may be considered to lie in a radial zone, thus at the zone of reflection, R, for such points is as follows:

Consider now the slightly difierent requirement, i.e., with a fixed maximum ratio, R, of central to reflector magnetic field intensities, the conditions which, in any case, a particle must satisfy to be reflected and effectively contained by the reflector field regions. If the particle possesses axial energy (W excessively large in relation to the energy perpendicular (W,) to the field, reflection will not occur, i.e., the reflector field region will usually be penetrated by the particle. Let the reflector field intensity be H and the central field be H then the maximum ratio of W /W which a particle may have and still be reflected comprises,

inn g1, Wm) m. Ho

In other Words all particles will be reflected by the gradientially intensified magnetic reflector field regions for which the first term, foregoing, does not exceed the second, viz.,

(III) R In this connection it is important to note that it is the ratio of energies that is significantnot the absolute values and also, it is the ratio of field intensities that controls, not the absolute value.

Having shown that particles whose ratio of parallel to perpendicular energy is less than a certain value will be contained by the reflector fields, the angle of exclusion of such fields can now be calculated. With reference to FIG. 2 of the drawing, given a particle velocity, v, the ratio of the parallel v to perpendicular, v components of the particle velocity defines an angle, 9, for which tan 6 "II where 0 must be greater than a minimum value, the angle of exclusion, in order for the particle to be reflected. We have then 1 (V) tan 92 for reflection As a consequence 1 (VI) sin 0 Z x R These results may now be used to compute the solid angle, using the relationships, shown in FIG. 3, of the drawing, into which particles may be lost at a reflector field and the albedo for an incident random distribution of particle velocities.

First:

Q=21r(1-cos 0) Accordingly, the solid angle 9 inside of which particles will be lost can be found from the relations above.

cos 6 V 1 sin% Therefore the fractional solid angle, L into which particles are lost per hemisphere must be As a corollary, some loss may be expected through the reflector regions, visualable as being through an orifice, not actually physical but as angular. An analogy is the angular cone of vision when looking upward from beneath the surface of a lake. Beyond a certain angle all light is internally reflected.

To compute the albedo, note that the flux of particles moving toward the reflector field is proportional to v for the individual particles, i.e., to find the ratio of particle flux entering to flux reflected We must include this factor in the calculation as the ratio,

(Flux reflected) Now:

(Flux incident) =21rfl n(v cos 0) sin 6d0 (Flux reflected) =21rL 'rL(v cos 0) sin ade where n number of particles, v =origina1 velocity.

L cos 0 sin 6(10 ..(IX) A-1 l HR This reflection coefficient is not particularly determinative of the reflector capabilities in the present intsance since the assumption is included that the distribution remains random. Actually the angular distribution of particle velocities will not be random as will be shown hereinatter due to the great length of the mean free paths in the present system; therefore, the actual reflection coefficient obtained in practice will be much better than this unduly pessimistic minimum.

The above relationships allow derivation. of a useful expression indicative of the transformation of energies and angles of the particle helices as they move from one part of the field to another, as follows:

This expression yields the energy ratio at any point in the field in terms of its value at another point.

Then

W v1 (w) R R [ch1 0+1] As before, angles 0 and 0' are to be measured with respect to the local field direction which at the peak reflector field will be parallel to the longitudinal axis. This relation will be employed hereinafter, in connection with the disclosure of methods of accomplishing fuel injection. Note then in X1, when R(x) 1, since the maximum value of sin 0' is 1, orbital path angles such that changes in the magnetic field. As a consequence it is found that is an adiabatic invariant for changes of H in time as well as space, the latter having been shown in the foregoing.

In accordance with Alfvn (Alfvn, H., Cosmical Electrodynamics, Oxford, University Press, New York, 1950), i.e., a first order theory is assigned, but noting that Kruskal has shown the results to be true to all orders in a perturbation expansion. For a path fixed in. space 1 E-cls= (standard generator equ-a-tlon) Here =1rr H=flux through an orbit of radius, r, at. any instant of time. Therefore the energy gain in one spiral revolution of the particle in the field is AW L The energy gain per unit time (second) is obtained. by dividing the above quantity by the units per revolution, i.e., the cyclotron period. We find this from the relation @f Hev r T c ILwa u w mc 20 dt H i lLfli fl dt T H d6 On integration, noting dW dH The final result is 1 (XII) constant The foregoing results demonstrate that, in all adiabatic changes of the kind described, the flux through the orbit circle of the particle remains constant, i.e.,

e W u-(m1) T) -constant v 1-= constant And also v H constant Now the product of two constants is also constant. Square the first and multiply by the reciprocal of the second.

H vfir constant r H constant i.e.,

(XIII) 1r7 H= constant Thus the flux through the orbit is a constant of motion, in the perturbation approximation.

While containment has been described with particular reference to the containment of positively charged ions, i.e., ionized single nuclei as is considered appropriate under thermonuclear reaction conditions, particularly, with high kinetic temperatures, the method is not limited to operation with such particles and in connection with thermonuclear reactions alone. With appropriately adaptive modification, considered apparent from the disclosure and especially with lower temperatures, e.g., below dissociation temperatures, negatively and positively-ionized particles formed by ionizing atoms, molecules, molecular residues and the like, by methods similar to those noted herein or by conventional methods, may also be contained. Since such contained particles may be given high kinetic energies it is contemplated in accordance with teachings of the invention that chemical reactions may be conducted in such a containment zone including many which cannot be conducted with ordinary procedures to produce known or hitherto unknown materials. This is believed especially true of those reactions which do not proceed at appreciable rates in present methods due to the excessive thermodynamic activation energies required.

Other highly desirable results may be obtained also, for example, as noted hereinafter, diffusion rates of various materials from the containment zone are materially different; therefore, it is apparent that separatory processes occur with mixed ions, e.g., different masses and/ or ratios of charge/mass if present in the containment zone. In general, such materials are subject to similar behavior as the positive ions in the operation of the invention, e.g., compression; therefore, it is to be expected that various procedures incorporating operations taught by the inven tion, when employed in chemical technology, will be found to be of considerable utility.

INJECTION Having disclosed, in the foregoing, factors which are determinative of containment, methods of effecting disposition of a thermonuclear fuel in the containment zone Will now be set forth. At the outset, it is to be noted that injection can be effected through one or both terminal reflector regions of the system or through the radial field region situated between the terminal regions and that the fuel will generally be in the form of an accelerated (preheated) space charge neutralized ionic beam directed at certain acceptance angles and with appropriate manipulation of the magnetic fields. Such injection will necessarily include the production of ionized particles and the acceleration thereof to at least the preheat temperature as by passage through an electrostatic voltage gradient or by equivalent accelerative treatment.

At the outset on elementary consideration of factors disclosed hereinbefore, it will be apparent that a particle directed from an external source through one of said reflector field regions and therefore having an axial velocity component suflicient to pass through the first reflector region, would also penetrate the second region and therefore not be contained, provided both reflector regions are similar in extent and magnetization intensity. Accordingly, with externally produced and accelerated ions, to acomplish particle trappingand accumulation in the containment zone, some procedure must be employed which effectively reduces the ratio of axial velocity to rotational velocity of the particle during transit through the containment zone in order for the particle to be reflected from the reflector regions, or, equivalently, increase the reflection capacity of the reflector fields during transit therebetween relative to the axial velocity of the particle. Ions produced, in situ, within the containment zone present a more simple problem since only containment factors, as described above, need be satisfied.

A preferred adiabetic injection, trapping and accumulation procedure which may be employed to effect disposition of a thermonuclear fuel charge in a containment zone of the character described above is described hereinafter. For the sake of simplicity a containment system will be considered in which the length of the reflector regions is short compared to the total length of the device as shown in idealized form in FIG. 4 of the drawing. As depicted therein a magnetic field of the general axial intensity profile shown in the lower graphical portion (b) of the figure, and which is caused to increase uniformly overall in intensity with the passage of time is established in the elongated cylindrical evacuated chamber 35 illustrated in portion (a) of said figure. Ion sources (not shown) are radially disposed about the longitudinal axis of the chamber 35 outwardly preferably from at least one reflector region, H so as to direct a beam of ionic fuel particles having a substantial kinetic energy axially whereby the individual ion follows a helical path inwardly into such reflector region, H similar to the typical particle path indicated at 36.

While it is usually preferred to dispose the ion sources axially outward from the containment zone, since various other structures, disclosed hereinafter, may then be more easily provided therein, it is equally feasible to dispose such sources radially about certain regions of the containment zone, i.e., in radial banks disposed concentrically about the containment zone between the reflector field regions. These centrally disposed ion sources may be employed either alone or with other described sources and methods of fuel injection described herein. With this central-radial arrangement, the ion beams may be directed semi-tangentially to the rotational orbits of the particles in the field providing a helical path of pitch angle determined similarly to that which is to be described with axial injection. With this injection method a rise in magnetic field intensity would be relied upon to cause the ion orbits to constrict whereby the ions would not strike the ion sources on rotation and/ or the pitch angle of injection may be adjusted so as to displace the beam sufficiently to effect this purpose with the assistance of a slow simultaneous increase in the magnetic field intensity.

However, preferred axial injection, as by utilizing ion sources disposed externally so as to direct energetic ions along axially oriented paths into a reflector field region, is accomplished, as follows:

At x=0, the peak of field H as indicated in FIG. 4, let

u( l( where l =cotangent 0=tangent P and P==pitch angle of helical path at injection, with relationships presented in the vectorial diagram of FIG. 5.

Then

vim/ .1 +0. 0)

With a particle having passed through the region, H i.e., the particle is at x=a, a point in the central field, H from an above noted relationship (X), for energy transformation there is obtained.

The particle travels thenceforth down to the far end of the containment zone, is reflected, in the region of H and returns to point, a, after a time interval, T. Now, as is known from the reflector field Equation II in order to be reflected the particle must have an energy ratio at, a, and after time, T, of

ll( y W But in the present case the magnetic field is caused to rise overall with time (in the present case it is arranged that the field is rising in such a way that R is constant) so that, since W constant magnetic field intensity will be linear for short intervals so that over any time interval, t,

dH(a) and Where )\=reciprocal of doubling time of field intensity. Therefore, during injection the following conditions must be satisfied.

demonstrating that injection pitch angles must be less than a certain value.

In general where B is a quantity greater than 1 and L=length of the containment zone.

. 18 Therefore the following conditions must be satisfied for trapping of the injected particle in the containment zone dH(a) R 5 To evaluate ,8 for the case under consideration, proceed as follows: From W constant and the energy transformation equation, there is obtained:

1 1/2 W) dermal which is the velocity most of the time.

Thus it is found that the condition for trapping of injected particles in the present case is,

dH(a) 1 :l1/2 2 dt 2H(a) 1 R 1+2 0 Now it can be seen that for most eificient injection 1( should be very much less than 1) so that The final expression indicating the condition for most efiieient injection and trapping of ions is', therefore, as follows:

This relationship can be used to determine a total trapping or fuel charge accumulation time, T, during which charged particles of a particular class may be injected and may be retained in the containment zone provided other subsidiary conditions are satisfied.

For a linearly rising field, H, at the end of a time interval, 7-,

At the particular time, when the injection condition just ceases to be satisfied for particles of given value of .5, the following holds:

Comparing the preceding two equations it is seen Time T is to be measured from the time that H is equal to zero. If H is begun with a finite value, somewhat later,

(XVI) then r is measured from the time found by extrapolating the linear rise time interval to the beginning or zero field. Injection can never be accomplished with an intensity, H 0, so that the actual injection time will always be less than -r. However the more rapidly the field is caused to rise the larger will be the fraction of rise time T, which is available for effective injection. For injection of particles with a range of values for $5 as between, 0 and E the effective trapping time Will be much larger than that which is indicated by the above expression.

An alternative method of injection can be employed in which the central regions (H of the containment field are maintained substantially constant or are allowed to increase relatively slowly in intensity While the intensity in the terminal reflector regions, H and H is caused to increase at a relatively greater rate, with the passage of time, as illustrated in FIG. 6 of the drawing.

As before (see FIG. 5 let .L( At time t=0 (neglecting the change in field intensity during the transit of particles from x=0 to x=a, in reflector field H and In this case the transit time interval, T, Will no longer be independent of time of injection, i.e., the transit time for a given particle will depend on the time, t, when it is injected so that and from the equations developed before,

i.e., since 20 then 1 0 1 1/2 2 n l nml T But R (t) gand 12(0) (H =being constant) Notice here that in H (O), the 0 refers to the time coordinate at which the particular particle was injected and not to the absolute zero of time when the reflector field originally began to increase in intensity.

dH R (t) 1 1/2 E (XVII) dt ZH I: R (0) 0 This expression is very similar to the one found for the first case noted above, except that one of the terms is a slowly varying function of the time. However, the rates of field rise required for adequate injection are comparable, and, therefore, the time intervals available for effective injection and trapping are comparable in the two methods. The foregoing calculations can be utilized to compute the approximate quantities of particles available for reaction at the termination of one injection cycle since the ratio of density at the end of injection to source beam density will be given approximately by the fuel accumulation time, 1-, divided by the one way transit time, i.e.,

or for large R,

(XVIII) where n is the density of the ions in the ion source beams.

The foregoing methods of disposing a thermonuclear fuel charge in a containment zone of the character described may be employed with particles of greatly varied energies thereby permitting great flexibility in the choice of injection energies and selection of operating conditions in the associated operations of the process. Particles may be injected and accumulated with low energies (ordinary thermal velocities) suitable, for example, as in chemical reactions, at intermediate energies wherein thermonuclear reactions would proceed only slowly or not appreciably or at high kinetic energies whereby appreciable thermonuclear reaction rates may be immediately obtained. In the event that thermonuclear fuel ions are injected at low or intermediate energies additional energy may be applied subsequently with densification (as described hereinafter) and as required to provide the conditions favorable for initiating and promoting the reaction.

Alternative and/ or auxiliary injection methods may be provided as, for example, by applying alternating electrostatic fields in the vicinity of the reflector regions by a method productive of an enhanced magnetic reflector field, ions may be injected and accumulated with or without variation of the magnetic field intensities; neutral atoms entering the plasma (once established), are

ionized and some fraction are retained therein, thus provision of a tenuous atmosphere (as by forming T from Li in the evacuated zone) or the injection of jets of appropriate gaseous forms of the thermonuclear fuel directed into the containment zone may constitute auxiliary injection methods; other manipulations of the reflector fields, e.g., outward translatory motion thereof during injection may also be employed to trap the ions; secondary accumulation zones established outwardly from a relatively diminished reflector region may serve to retain fuel ions lost from the primary reaction zone and to accumulate newly injected material, thereafter to be reintroduced into the reaction zone, and other equivalent methods may also be employed.

Furthermore, once the reaction is proceeding as under compression, noted hereinafter, fuel ions accelerated to kinetic temperatures (energies) equivalent to or above those at which the reaction proceeds with appreciable vigor, may be injected and trapped as by methods described above so as to aid in sustaining the reaction by replenishing fuel and perhaps effectively increasing ionic temperatures. In this manner, and/or with those described above, the length of the combustion cycle may be increased to the point that depletion of the fuel ceases to be a factor determinative of the period during which a reaction will continue.

COMPRESSION Due to the peculiar nature of the magnetic fields employed to establish the containment zone, as noted hereinbefore, two somewhat separable containment modes are provided, (1) a radial containment along the length of the zone, and (2), axial containment or closure pro vided by the gradientially-intensified magnetic reflector field regions. Similarly, compression is divisible into radial and axial components or modes, radial compression being obtained whenever a portion of the magnetic field enclosing an appreciable plasma volume is intensified and axial compression being obtained by inward translatory motion of the position of at least one of said reflector field (also, intensification of the reflector field regions producing an axial bulging of the field region also shortens the path length therebetween and thereby produces some axial compression).

The term compression as employed herein is intended to relate to the process wherein a contained plasma is transformed from a tenuous state into a more dense state with attendant increase in the kinetic energy of the contained particles, containment pressure increase and other properties analogous to ordinary gas compression. Accordingly, the compression process may be considered to involve initial and final containment states corresponding to the containment of relatively low and relatively higher density plasmas and, likewise, particles of low and higher kinetic energies. Moreover, compression provides an ideal, exceedingly useful, means of converting a tenuous, low-kinetic energy (temperature) plasma into a densified plasma wherein at least a large proportion of the particles have a high kinetic energy, thereby to initiate and promote a thermonuclear reaction in a fuel plasma provided as described hereinbefore. Maintenance of a compressive state at any particular level will, therefore, constitute a state of containment and such a state of containment, if sustained following initiation of the thermonuclear reaction, provides a means for maintaining such a reaction for a considerable period and at a corresponding rate, i.e., regulation of the compression controls the reaction rate. Moreover, maintenance of the compressive containment state following initiation of the reaction allows replenishment of the fuel plasma as it is depleted, as described hereinbefore, with long reaction periods then being feasible.

Large thermonuclear power and other product outputs from reasonably small volumes of containment zone require, as indicated by reaction kinetics, considered here- 22 inafter, particle densities of the order of 10 particles per cc. and correspondingly high kinetic temperatures, conditions provided simultaneously by compression of tenuous fuel charges; however, reactions, thermonuclear or chemical, at lower and higher densities and/or kinetic temperatures are also useful.

Compression may be employed for other purposes. For example, the compressive method, particularly the radial mode, described herein may be applied to shape or confine the region occupied by the plasma and/ or with appropriate manipulation of the reflector fields, to move the plasma from one location to another in the evacuated region. In this manner the contained plasma may be restrained from striking structures disposed in the evacuated region, the plasma may be formed in a particular locale and transported for more efficient use into another area and other plasma manipulations as considered apparent from the disclosure.

The following portions of the disclosure will describe the compressive process as occurring after a relatively rapid injection period employed to dispose a more or less fixed quantity of fuel ions in the containment zone, such fuel ions being heated generally to an intermediate kinetic temperature as noted above; however, it will be understood that compression may be applied at any temperature level or may be applied for containment of ions injected at high kinetic temperatures whereby the reaction may proceed immediately, i.e., as soon as sufficient ion density is obtained.

RADIAL COMPRESSION With the foregoing in mind, consider now the process of radial compression of a plasma disposed in the containment zone and its optimization. As noted above, radim compression is obtained whenever the magnetic field is intensified along a substantial length of the containment zone, e.g., as by increasing the electrical current in a solenoidal winding, distributed along a length of the containment zone. An approximate derivation of the equations for radial compression will be made at the outset with reference, later, to more general verifications of the phenomenon. First consider the motion of a particle in crossed electric and magnetic fields. If a particle is moving in a magnetic field, H, and is subjected to an electric field, B, it can be shown that the center of rotation of the particle will drift with a velocity given by the equation,

This velocity is independent of the charge or the mass of the particle and consists of a cycloidal motion of the particle perpendicular to E and H; towever, the relative direction of rotation will be dependent on the sign, positive or negative, of the charge on the particle as indicated in the accompanying FIG. 7.

Now consider an axially symmetrical magnetic field system where the field strength, H, is varying as a function of time. If the field is increasing with time there must be an electric field associated (since, fH-dA, is changing) and the electric field will appear as circular a force lines, E, as shown in accompanying FIG. 8, wherein dt H 

1. IN A PROCESS WHEREIN A PLASMA OF ENERGETIC ION AND NEUTRALIZING ELECTRONS IS PRODUCED, THE STEPS COMPRISING PROVIDING AN AXIALLY SYMMETRIC MAGNETIC FIELD IN AN EVACUATED REGION TO RADIALLY DEFINE A ZONE IN SAID FIELD, ESTABLISHING GRADIENTIALLY-INTENSIFIED REFLECTOR FIELD REGIONS AT SPACED POSITIONS IN SAID FIELD TO SERVE AS CLOSURES FOR SAID ZONE EFFECTIVE FOR CONFINING SAID PLASMA THEREIN, AND DIRECTING A SPACE CHARGE NEUTRALIZED ION BEAM INTO SAID ZONE FOR CONFINEMENT THEREIN. 